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Factor the expression (x+y)(2m-n) - m(x+y).

Mathematics

ScanSolve AI Answer

Answer

(x+y)(m-n)

Step-by-step solution

4 steps

  1. Identify the common factor in the expression.

    The expression is (x+y)(2m−n)−m(x+y)(x+y)(2m-n) - m(x+y).
    The term (x+y)(x+y) is common to both parts of the expression.

  2. Factor out the common term (x+y)(x+y).

    (x+y)(2m−n)−m(x+y)=(x+y)[(2m−n)−m](x+y)(2m-n) - m(x+y) = (x+y) [ (2m-n) - m ]

  3. Simplify the expression inside the square brackets.

    (2m−n)−m=2m−n−m=m−n(2m-n) - m = 2m - n - m = m - n

  4. Write the completely factorized expression.

    (x+y)(m−n)(x+y)(m-n)
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